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At 3:25, the smaller angle formed between the two hands of a clock is ____.
- a)Obtuse
- b)Acute
- c)Right
- d)None of these
Correct answer is option 'B'. Can you explain this answer?
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At 3:25, the smaller angle formed between the two hands of a clock is ...
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At 3:25, the smaller angle formed between the two hands of a clock is ...
Explanation:
To determine the angle between the two hands of a clock at a specific time, we need to understand the movement of the hands.
The Hour Hand:
- The hour hand completes a full rotation in 12 hours.
- In 1 hour, the hour hand moves 30 degrees (360/12).
- In 1 minute, the hour hand moves 0.5 degrees (30/60).
The Minute Hand:
- The minute hand completes a full rotation in 60 minutes.
- In 1 minute, the minute hand moves 6 degrees (360/60).
Now, let's calculate the angle between the two hands at 3:25.
Position of the Hour Hand:
- At 3:00, the hour hand points directly at the number 3.
- In 25 minutes, the hour hand moves (25 * 0.5) = 12.5 degrees.
Position of the Minute Hand:
- At 25 minutes, the minute hand points directly at the number 5.
- In 25 minutes, the minute hand moves (25 * 6) = 150 degrees.
Angle between the Hands:
To find the smaller angle between the hands, we need to subtract the smaller angle from the larger angle.
- In this case, the hour hand is at 12.5 degrees and the minute hand is at 150 degrees.
- The smaller angle between the hands is |12.5 - 150| = 137.5 degrees.
Since the angle between the hands is greater than 90 degrees, it is considered an obtuse angle.
Therefore, the correct answer is Option A: Obtuse.
To determine the angle between the two hands of a clock at a specific time, we need to understand the movement of the hands.
The Hour Hand:
- The hour hand completes a full rotation in 12 hours.
- In 1 hour, the hour hand moves 30 degrees (360/12).
- In 1 minute, the hour hand moves 0.5 degrees (30/60).
The Minute Hand:
- The minute hand completes a full rotation in 60 minutes.
- In 1 minute, the minute hand moves 6 degrees (360/60).
Now, let's calculate the angle between the two hands at 3:25.
Position of the Hour Hand:
- At 3:00, the hour hand points directly at the number 3.
- In 25 minutes, the hour hand moves (25 * 0.5) = 12.5 degrees.
Position of the Minute Hand:
- At 25 minutes, the minute hand points directly at the number 5.
- In 25 minutes, the minute hand moves (25 * 6) = 150 degrees.
Angle between the Hands:
To find the smaller angle between the hands, we need to subtract the smaller angle from the larger angle.
- In this case, the hour hand is at 12.5 degrees and the minute hand is at 150 degrees.
- The smaller angle between the hands is |12.5 - 150| = 137.5 degrees.
Since the angle between the hands is greater than 90 degrees, it is considered an obtuse angle.
Therefore, the correct answer is Option A: Obtuse.
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At 3:25, the smaller angle formed between the two hands of a clock is ...
Ans b. Acute angle
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